This paper is concerned with the modeling and control of processes with input dynamic nonlinearity. Rather than modeling the overall process with a nonlinear model, it is proposed to represent the process by a composite model of a linear model (LM) and a feedforward neural network (FNN). The LM is to capture the dominant linear dynamics, while the FNN is to approximate the remaining nonlinear dynamics. The controller, in correspondence, consists of two sub-controllers: a linear predictive controller (LPC) designed based on the LM, and an iterative inversion controller (IIC) designed based on the FNN. These two sub-controllers work together in a cascade fashion that the LPC computes the desired reference input to the IIC via an analytic predictive control algorithm and the IIC then determines the process manipulated variable. Since the neural network is used to model the nonlinear dynamics only, not the overall process, a relatively small sized network is required, thus reducing computational requirement. The combination of linear and nonlinear controls results in a simple and effective controller for a class of nonlinear processes, as illustrated by the simulations in this paper.